Subtract $ \dfrac{3}{4} $ from $ 12x^3+4x^2 $ to get $ \dfrac{ \color{purple}{ 48x^3+16x^2-3 } }{ 4 }$.

Step 1: Write $ 12x^3+4x^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 4 }$.

$$ \begin{aligned} 12x^3+4x^2- \frac{3}{4} & \xlongequal{\text{Step 1}} \frac{12x^3+4x^2}{\color{red}{1}} - \frac{3}{4} = \frac{ \left( 12x^3+4x^2 \right) \cdot \color{blue}{ 4 }}{ 1 \cdot \color{blue}{ 4 }} - \frac{ 3 }{ 4 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 48x^3+16x^2 } }{ 4 } - \frac{ \color{purple}{ 3 } }{ 4 }=\frac{ \color{purple}{ 48x^3+16x^2-3 } }{ 4 } \end{aligned} $$